Protein motors use chemical and electrochemical energy to generate mechanical forces. These forces drive intracellular motions that perform a variety of cellular functions; e.g., manufacturing ATP, pumping ions, shuttling proteins and chromosomes and extending cellular protrusions. Thus, the operating principles of these molecular machines are central to cellular physiology. Recent advances permit measuring forces and motions of single macromolecules on the scale of piconewtons and nanometers, and structural studies are revealing the detailed molecular architecture of protein motors. This has renewed the search for the physical principles that underlie mechanochemical energy conversion in macromolecular systems. It is now possible to make realistic models of molecular mechanochemical processes which can be related directly to observations, and which therefore can be tested experimentally. This project involves the construction of mathematical models to describe several important classes of molecular motors driven by nucleotide hydrolysis and transmembrane electromotive gradients. The particular systems to be addressed are (1) the V-ATPase ion pumps; (2)the bacterial flagellar motor; (3) the kinesin family; (4) the physical mechanisms that regulate the lamellipodial rotrusion motor of motile cells and the localization of membrane proteins that control these mechanochemical processes, and (5) the role of the fluid environment in molecular mechanochemical processes. Specifically, because many biomolecular motors operate in an aqueous environment and are mesoscopic in scale (large compared to water molecules but still small enough for Brownian motion to be important), Dr. Oster also proposes to develop computational methods for mesoscale biofluid dynamics with immersed molecular machinery. Such methods will also provide a means of studying intracellular water movements driven by osmotic forces. The proposed approach in each case is to begin by formulating stochastic equations that describe the mechanical behavior of the molecular structures. These equations are then subject to mathematical analyses where possible, and to numerical simulations in which parameters have been chosen using the best available experimental data. Results will be compared to data supplied by experimental collaborators and colleagues. Computer animations and other visual techniques will be used to present results in a broadly understandable manner.